The typing does change when when the form is changed. When it changes into a fridge, it's ice type. When it is a Fan, then its flying type. The typing doesn't stay the same. Try to not get muddled up. However, the second type does stay the same, electric, I think that is what you might be getting confused about.

Maybe You are asking of the forms changing in the pokedex.
That changes only when the wanted form is selscted to keep as default ( the thing to do when you open the forms in the pokedex start the sprite,) there is an option to turn over the forms. This way the pokedex will show what the type is set a s default like
If you set the fridge form to be the default the pokedex will show the fridge form and electric ice type!